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The TGD based vision about how the arrow of geometric time is by no
means fully developed and final.
- What seems clear now is the decisive role of
ZEO and hierarchy of CDs, and the fact that the quantum arrow of
geometric time is coded into the structure of zero energy states to a
high extent. The still questionable but attractively simple hypothesis
is that U matrix two basis with opposite quantum arrows of geometric
time: is this assumption really consistent with what we know about the
arrow of time? If this is the case, the question is how the relatively
well-defined quantum arrow of geometric time implies the experienced
arrow of geometric time. Should one assume the arrow of geometric
time separately as a basic property of the state function reduction
cascade or more economically- does it follow from the arrow of time
for zero energy states?
- The state function reductions occur alternately at the two
boundaries of CD. If the reduction occurs at given boundary is
immediately followed by a reduction at the opposite boundary, the arrow
of time alternates: this does not conform with intuitive expectations:
for instance, this would imply that there are two selves assignable to
the opposite boundaries!
Zero energy states are however de-localized in the moduli space CDs
(size of CD plus discrete subgroup of Lorentz group defining boosts of
CD leaving second tip invariant). One has quantum superposition of
CDs with difference scales but with fixed upper or lower boundary
belonging to the same light-cone boundary after state function
reduction. In standard quantum measurement theory the repetition of
state function reduction does not change the state but now it would give
rise to the experienced flow of time. Zeno effect indeed requires that
state function reductions can occur repeatedly at the same boundary. In
these reductions the wave function in moduli degrees of freedom of CD
changes. This implies "dispersion" in the moduli space of CDs
experienced as flow of time with definite arrow.
- This approach codes also the arrow of time at the space-time
level: the average space-time sheet in quantum superposition increases
in size as the average position of the "upper boundary" of CDs drifts
towards future state function reduction by state function reduction.
- In principle the arrow of time can temporarily change but it
would seem that this can occur in very special circumstances and
probably takes place in living matter. Phase conjugate laser beam is a
non-biological example in this respect.
This proposal involves minimal number of assumptions and is the most
convincing one found hitherto and the challenge is to invent objections
in order to develop it in more detail.
For details and background see the chapter "About nature of time".
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